On Sat, Jan 30, 2010 at 1:24 AM, Conal Elliott <conal at conal.net> wrote:
> I call it "an m" or (more specifically) "an Int m" or "a list of Int". For
> instance, "a list" or "an Int list" or "a list of Int". - Conal
>>> On Wed, Jan 27, 2010 at 12:14 PM, Luke Palmer <lrpalmer at gmail.com> wrote:
>>> On Wed, Jan 27, 2010 at 11:39 AM, Jochem Berndsen <jochem at functor.nl>
>> wrote:
>> >> Now, here's the question: Is is correct to say that [3, 5, 8] is a
>> >> monad?
>> >
>> > In what sense would this be a monad? I don't quite get your question.
>>>> I think the question is this: if m is a monad, then what do you call
>> a thing of type m Int, or m Whatever.
>>>> Luke
>>>Conal's is the most sensible approach - "what do you call it" amounts to
"what sort of a thing is it", and the best we can say in that respect is
"er, its a thing of type m Whatever". (My preference, if maximal
explicitness is needed, is to say "it's a token of its type"; some say "term
of type m Whatever".) Trying to classify such a thing as "value", "object",
"computation", "reduction" etc. inevitably (and necessarily) leads to
tail-chasing since those notions are all essentially equivalent. Plus they
miss the essential point, which is the typing.
Original poster would probably find Martin-Lof's philosophically-tinged
writings very good on this - clear, reasonably simple, and revelatory, if
you've never closely looked at intuitionistic logic before. Truth of a
proposition, evidence of a judgment, validity of a
proof<http://www.jstor.org/pss/20116466>is especially readable, as is
On
the meanings of the Logical Constants and the Justifications of the Logical
Laws <http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no1/meaning/meaning.html>.
Presents a completely new (to me) way of thinking about "what is it,
really?" questions about computation, monads, etc., i.e. ask not "what is
it?" but "how do you know?" or even "how do you make it?" The Stanford
article on types and
tokens<http://plato.stanford.edu/entries/types-tokens/>is also very
enlightening in this respect.
-g
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